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bubbers
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. Homework Statement
The tension T in the string of the yo-yo is given by:
T=(mgR)/(2r^2+R^2)
where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm to 0.8cm. Does the tension increase or decrease?
I assume you'd need
dT=∂T/∂r*dr + ∂T/∂R*dR
I'm not completely sure how to approach this problem. My guess is that you need to find the partials, and then use the values to which r and R increase somehow, maybe as dr and dR values...but I'm not sure how to go about that.
Any help would be greatly appreciated :)
The tension T in the string of the yo-yo is given by:
T=(mgR)/(2r^2+R^2)
where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm to 0.8cm. Does the tension increase or decrease?
Homework Equations
I assume you'd need
dT=∂T/∂r*dr + ∂T/∂R*dR
The Attempt at a Solution
I'm not completely sure how to approach this problem. My guess is that you need to find the partials, and then use the values to which r and R increase somehow, maybe as dr and dR values...but I'm not sure how to go about that.
Any help would be greatly appreciated :)